TY - JOUR T1 - Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion AU - Peng , Yarong AU - Li , Zhi AU - Xu , Liping JO - Annals of Applied Mathematics VL - 4 SP - 414 EP - 440 PY - 2022 DA - 2022/11 SN - 38 DO - http://doi.org/10.4208/aam.OA-2021-0082 UR - https://global-sci.org/intro/article_detail/aam/21165.html KW - Global attracting set, quasi-invariant sets, tempered fractional Brownian motion, exponential decay. AB -

In this paper, we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space. We obtain the global attracting and quasi-invariant sets of the considered equations driven by tempered fractional Brownian motion $B^{α,λ}(t)$ with $0<α<1/2$ and $λ>0.$ In particular, we give some sufficient conditions which ensure the exponential decay in the $p$-th moment of the mild solution of the considered equations. Finally, an example is given to illustrate the feasibility and effectiveness of the results obtained.